Topological Classification and Stability of Fermi Surfaces

TL;DR

This paper classifies Fermi surfaces using topological charges within the Cartan framework, revealing six types of charges that confer robustness against symmetry-preserving perturbations.

Contribution

It introduces a topological classification of Fermi surfaces based on their Hamiltonian's Cartan class, identifying six topological charges and their symmetry relations.

Findings

Six types of topological charges identified.

Topological charges form two symmetry-based groups.

Fermi surfaces are protected by these topological charges.

Abstract

In the framework of the Cartan classification of Hamiltonians, a kind of topological classification of Fermi surfaces is established in terms of topological charges. The topological charge of a Fermi surface depends on its codimension and the class to which its Hamiltonian belongs. It is revealed that six types of topological charges exist, and they form two groups with respect to the chiral symmetry, with each group consisting of one original charge and two descendants. It is these nontrivial topological charges which lead to the robust topological protection of the corresponding Fermi surfaces against perturbations that preserve discrete symmetries.